PDE: uf = 2ихх, 0 < х < 1, t> 0 0 0 ВС: и (0, t) — —1, иx(1,t) — 1 3πχ IC: и (х, 0) — х + sin - 1 2
PDE: uf = 2ихх, 0 < х < 1, t> 0 0 0 ВС: и (0, t) — —1, иx(1,t) — 1 3πχ IC: и (х, 0) — х + sin - 1 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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need some help with partial diff equations.
Transcribed Image Text:PDE: uf =
2ихх, 0 < х < 1, t> 0
0 <x< 1, t > 0
ВС: и (0, t) —
—1, иx(1,t) — 1
3πχ
IC: и (х, 0) — х + sin
- 1
2
Expert Solution
Step 1
Claim: solution for the heat equation:
Let us use separation of variables. Let u(x,t)=X(x)T(t).
Then 4ut=uxx becomes X(x)T’(t)=X’’(x)T(t).
We divide both sides by X(x)T(t) to obtain:
where λ is a constant.
The boundary conditions are:
Integrating both sides
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